This document discusses derivatives and their applications. It presents examples of using the Mean Value Theorem to find values within an interval where the derivative is equal to the slope of the tangent line. It also gives examples of taking the derivative of different functions and finding the parent function given its derivative. Finally, it asks if a general rule can be determined for the derivatives of all power functions.

1. Auntie Derivative and
her Family of Functions
flickr derivatives 6

2. Find the number in the given interval which satisfies the conclusion of the
Mean Value Theorem.
x = -0.9012084345
x = .3062145833
x = 15.49848984
x = 40.63366242

4. Find the derivative of each of the following:
Given the following derivative, determine the parent function:
Can you generalize a rule
for all power functions?